Question

given d=5 S9=75 find a&a9​

Answer 1

d=5

n=9

Now

Since,

S9=75

$\frac{n}{2} (2a + (n - 1)d) = 75 \\ \frac{9}{2} (2a + (9 - 1) \times 5) =75 \\ \frac{9}{2}(2a + 8 \times 5) = 75 \\ \frac{9}{2} (2a + 40) = 75 \\ 9(a + 20) = 75 \\ a + 20 = \frac{75}{9} \\ a + 20 = \frac{25}{3} \\ a = \frac{25}{3} - 20 \\ = \frac{25 - 60}{3} \\ a= \frac{ - 35}{3}$

$a9 = a + (9 - 1)d \\ = \frac{ - 35}{3} + 8 \times 5 \\ = \frac{ - 35}{3} + 40 \\ = \frac{ - 35 + 120}{3 } \\ a9 = \frac{85}{3}$

Hope it is helpful